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# If w + z = 28, what is the value of wz

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If w + z = 28, what is the value of wz [#permalink]

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22 Mar 2013, 10:14
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If w + z = 28, what is the value of wz

(1) w and z are positive integers
(2) w and z are consecutive odd integers
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Mar 2013, 13:19, edited 1 time in total.
Edited the question.
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Re: if w + Z = 28, what is the value of wz [#permalink]

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22 Mar 2013, 12:13
4
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No problemo!

Just to clarify one thing. Two consecutive odd numbers adding up to 28 must be 13 and 15, but if the numbers get unwieldy, such as w+z = 280, just divide the sum by 2 and then take the numbers on either side. In other words, the two numbers need to average out to that, so it would be 139 and 141 in this example. Obviously, since this is the GMAT, the numbers will lead you to an even integer so you can take the odd ones on either side.

This is the same principle for dividing by 3 or any other number, you just need to divide by the number of terms. Ex: w + x + z = 279. What are the 3 consecutive odd integers that form w, x and z: 279 /3 = 93. The three odd numbers would be 91, 93 and 95, so that they average out to 93.

Hope this helps on questions like this when the numbers aren't so easy to spot!
-Ron
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Re: if w + Z = 28, what is the value of wz [#permalink]

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22 Mar 2013, 11:21
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GMAThirst wrote:
if w + Z = 28, what is the value of wz

1. w and z are positive integers
2. w and z are consecutive odd integers

Hi GMAThirst, let's examine these statements one at a time:

1. w and z are positive integers.
We know that both must be positive, so this eliminates 30 and -2, but it could be 1 and 27, 2 and 26, 3 and 25, etc. All of which have different products (1x27=27, 2x26=52, etc) A is insufficient on its own

2. w and z are consecutive odd integers
This would have to be 13 and 15. No other positive consecutive odd integers would add up to 28. Statement A makes us wonder about negative numbers, what about -13 and -15? Well they would add up to -28, which isn't the same as +28, so they're out as possibilities. What about other negative consecutive odd integers? Nothing is ever going to give you anything other than a negative number, so no negative numbers could work here. Statement 2 is thus sufficient on its own, with no need to bring in statement #1. (w*z must be either 13*15 or 15*13, either way giving the answer of 195 by commutativity)

Hope this helps!
-Ron
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Re: if w + Z = 28, what is the value of wz [#permalink]

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22 Mar 2013, 11:21
1. w and z are positive integers; thay can be any number < 27 as long as w+z=28

$$w=1, z=27$$

$$wz=27$$

$$w=2 ,z=26$$

$$wz=52$$

$$....$$

Not sufficient

2. w and z are consecutive odd integers; so they can be only 15 and 13

$$w=13, z =15$$

$$wz=195$$

$$z=13 ,w =15$$

$$wz=195$$

Sufficient

B
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Re: if w + Z = 28, what is the value of wz [#permalink]

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22 Mar 2013, 11:47
Thanks VeritasPrepRon
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Re: If w + z = 28, what is the value of wz [#permalink]

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22 Mar 2013, 13:23
Expert's post
If w + z = 28, what is the value of wz

(1) w and z are positive integers. Infinitely many values are possible for w and z, for example: ..., (-1, 29), (0, 28), (1, 27), ... Not sufficient.

(2) w and z are consecutive odd integers. So, we have that 28 is the sum of two consecutive odd integers: x+(x+2)=28 (where x is an odd integer) --> x=13. So, either w=13 and z=15 OR w=15 and z=13. In any case, wz=13*15. Sufficient.

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Re: If w + z = 28, what is the value of wz [#permalink]

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19 Jul 2013, 00:47
Quote:
(1) w and z are positive integers
(2) w and z are consecutive odd integers

I understand why statment 2 alone is sufficent in this example, but what if we were told that "w + z = $$|28|$$" would that mean the answer is C as statment 2 in itself is insufficent (w and z could be -15, -13 or 13, 15) but with statment 1 we can solve the stem (since only 13 and 15 are left).

Have I understood it correctly?
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Re: If w + z = 28, what is the value of wz [#permalink]

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19 Jul 2013, 01:02
Expert's post
aeglorre wrote:
Quote:
(1) w and z are positive integers
(2) w and z are consecutive odd integers

I understand why statment 2 alone is sufficent in this example, but what if we were told that "w + z = $$|28|$$" would that mean the answer is C as statment 2 in itself is insufficent (w and z could be -15, -13 or 13, 15) but with statment 1 we can solve the stem (since only 13 and 15 are left).

Have I understood it correctly?

No. |28|=28, so w + z = |28| is the same as w + z = 28.

Guess, you meant: |w + z| = 28. Now, if the question were: "|w + z| = 28, what is the value of wz?", the correct answer would still be B. From |w + z| = 28 and w and z are consecutive odd integers, it follows that the integers can be 13 and 15 OR -13 and -15. In any case wz = 195.

Hope it's clear.
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Re: If w + z = 28, what is the value of wz [#permalink]

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19 Jul 2013, 01:08
Bunuel wrote:
aeglorre wrote:
Quote:
(1) w and z are positive integers
(2) w and z are consecutive odd integers

I understand why statment 2 alone is sufficent in this example, but what if we were told that "w + z = $$|28|$$" would that mean the answer is C as statment 2 in itself is insufficent (w and z could be -15, -13 or 13, 15) but with statment 1 we can solve the stem (since only 13 and 15 are left).

Have I understood it correctly?

No. |28|=28, so w + z = |28| is the same as w + z = 28.

Guess, you meant: |w + z| = 28. Now, if the question were: "|w + z| = 28, what is the value of wz?", the correct answer would still be B. From |w + z| = 28 and w and z are consecutive odd integers, it follows that the integers can be 13 and 15 OR -13 and -15. In any case wz = 195.

Hope it's clear.

It is very clear - in my assumption I completely missed that what they asked was not for me to know what w and z in theirselves are, but what the PRODUCT of the two is. Since the PRODUCT of the two is the same irrespective of if both are positive or negative, B is sufficent.

Thanks a lot, there are severe flaws in my understanding, intuition and knowledge of concept but you're helping me a great deal.
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Re: if w + Z = 28, what is the value of wz [#permalink]

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30 Nov 2013, 18:51
VeritasPrepRon wrote:
GMAThirst wrote:
if w + Z = 28, what is the value of wz

1. w and z are positive integers
2. w and z are consecutive odd integers

Hi GMAThirst, let's examine these statements one at a time:

1. w and z are positive integers.
We know that both must be positive, so this eliminates 30 and -2, but it could be 1 and 27, 2 and 26, 3 and 25, etc. All of which have different products (1x27=27, 2x26=52, etc) A is insufficient on its own

2. w and z are consecutive odd integers
This would have to be 13 and 15. No other positive consecutive odd integers would add up to 28. Statement A makes us wonder about negative numbers, what about -13 and -15? Well they would add up to -28, which isn't the same as +28, so they're out as possibilities. What about other negative consecutive odd integers? Nothing is ever going to give you anything other than a negative number, so no negative numbers could work here. Statement 2 is thus sufficient on its own, with no need to bring in statement #1. (w*z must be either 13*15 or 15*13, either way giving the answer of 195 by commutativity)

Hope this helps!
-Ron

But statement 2 does not say anything about positive or negative odd integers.So why we are considering positive consecutive odd integers here.In that way are we not taking statement 1 into consideration and which leads to answer C?
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Re: if w + Z = 28, what is the value of wz [#permalink]

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01 Dec 2013, 07:17
Expert's post
sunita123 wrote:
VeritasPrepRon wrote:
GMAThirst wrote:
if w + Z = 28, what is the value of wz

1. w and z are positive integers
2. w and z are consecutive odd integers

Hi GMAThirst, let's examine these statements one at a time:

1. w and z are positive integers.
We know that both must be positive, so this eliminates 30 and -2, but it could be 1 and 27, 2 and 26, 3 and 25, etc. All of which have different products (1x27=27, 2x26=52, etc) A is insufficient on its own

2. w and z are consecutive odd integers
This would have to be 13 and 15. No other positive consecutive odd integers would add up to 28. Statement A makes us wonder about negative numbers, what about -13 and -15? Well they would add up to -28, which isn't the same as +28, so they're out as possibilities. What about other negative consecutive odd integers? Nothing is ever going to give you anything other than a negative number, so no negative numbers could work here. Statement 2 is thus sufficient on its own, with no need to bring in statement #1. (w*z must be either 13*15 or 15*13, either way giving the answer of 195 by commutativity)

Hope this helps!
-Ron

But statement 2 does not say anything about positive or negative odd integers.So why we are considering positive consecutive odd integers here.In that way are we not taking statement 1 into consideration and which leads to answer C?

Please check here: if-w-z-28-what-is-the-value-of-wz-149627.html#p1201241 You can see there that we can find w and z even not knowing their signs.
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Re: If w + z = 28, what is the value of wz [#permalink]

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Re: If w + z = 28, what is the value of wz   [#permalink] 02 Apr 2016, 00:55
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# If w + z = 28, what is the value of wz

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